You're estimating costs for a new power line with your...

You're estimating costs for a new power line with your company's financial group. Engineering specifies a resistance of $50 \mathrm{~m} \Omega$ per kilometer for the line. The costs and densities of copper and aluminum are, respectively, \$6.86/kg and $8.9 \mathrm{~g} / \mathrm{cm}^{3}$, and \$2.23/kg and $2.7 \mathrm{~g} / \mathrm{cm}^{3}$. Determine the cost per meter of each type of wire. Which is more economical?

Key Concepts

Comparative Economic Evaluation

This concept refers to assessing the cost-effectiveness of alternative materials by comparing the calculated cost per meter for each option. It involves weighing material and performance trade-offs to determine which option is more economical for the specified requirements.

Electrical Resistance and Conductor Geometry

This concept involves understanding how the resistance of a wire depends on its material resistivity, length, and cross-sectional area. In problems where a specified resistance per unit length is required, the designer must determine the necessary cross-sectional area of the conductor, which directly influences both the electrical performance and the material usage.

Material Properties and Density

Material properties such as electrical resistivity and density are critical in conductor design. Density is used to convert between volume and mass, allowing for the calculation of how much raw material is required per unit length of conductor. Material density, together with the cost per unit mass, influences the overall cost calculation for each type of conductor.

Cost Analysis

Cost analysis in this context involves calculating the overall cost per meter of the conductor by combining the mass of material needed (derived from its density and required volume) with the material's cost per unit mass. This allows for a direct comparison of different materials based on their economic impact while meeting the electrical performance criteria.

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